Pair Of Automata Research Articles

Simulation of the Motion of Magnetic Nanoparticles in Human Tissues

In this paper an attempt on the basis of the theory of mobile cellular automata to develop a model of motion of magnetic nanoparticles in human organs and tissues. In the framework of the method of movable cellular automata, the simulated system (tissues and organs) is represented by an assembly of interacting automata (elements of finite size). The concept of the method is based on the introduction of a new state type – the state of a pair of automata. Setting various parameters of the medium (tissues and organs). We can vary behavior of these particles in these mediums.

Formal Verification Strategy for Statechart based Design of Reconfigurable Control of High Integrity Reactive Systems

Automated high integrity reactive systems required in the control of defence, automotive, rapid mass transport, manufacturing and healthcare systems, among many others, accentuate the need for formal specification and design tools. Reconfigurability by design is an added requirement given the costly development processes. Many of these systems are hybrids of discrete event and continuous-time subsystems. Statecharts (implemented as stateflow in Matlab) are increasingly being proposed as the language of choice for the discrete-event part. However, the complex semantics of statecharts make automated formal verification difficult and hence largely an unresolved problem. Formal verification, in preference to simulation/testing, is necessary to specify these systems at the required level of integrity and to maintain traceability along the different phases of design and operation. Drawing from a number of different approaches by others to develop formal semantics at requirement and implementation levels, a first attempt was made by the author to develop a modular formal verification strategy applicable to statechart based controller specifications for complex reactive systems and an early version of the original approach, which was completely based on regular languages (hence, finite state automata) and different compositions thereof, was published in 2005.The key idea was the implementation of these composition operations through suitably interpreted port structures between pairs of automata resulting from a decomposition of the statechart. Application development based on this model has been done with collaborators on an elevator test rig built for the purpose and still continuing. While many of the under lying concepts are still valid and there is much to be learnt from their practical implementation and extension, there are fundamental limitations in this model stemming from the rather basic computational and expressive power of regular languages. In the current paper the author attempts to extend the method to context­ free language based models (hence, pushdown automata, PDA) to include real-time semantics for internal (fast) events and general correctness properties expressed in temporal logic, posed as supervisory specifications of Ramage-Wonham type interpreted on the port structures between pairs of PDA whenever possible. It is shown that decidability problems limit this choice to restricted forms of context-free languages, and the development is done with Event-dock Visibly Pushdown Automata (ECVPA), which are dosed under Boolean operations and determinisable. The ECVPA based verification model is presented with high-speed railway signalling as a target environment.

CSP is a retract of CCS

Automata theory provides two ways of defining an automaton: either by its transition system, defining its states and events, or by its language, the set of sequences (traces) of events in which it can engage. For many classes of automaton, these forms of definition have been proved equivalent. For example, there is a well-known isomorphism between regular languages and finite deterministic automata. This paper suggests that for (demonically) the non-deterministic automata (as treated in process algebra), the appropriate link between transition systems and languages may be a retraction rather than an isomorphism. A pair of automata, defined in the tradition of CCS by their transition systems, may be compared by a pre-ordering based on some kind of simulation or bisimulation, for example, weak, strong, or barbed. Automata defined in the tradition of CSP are naturally ordered by set inclusion of their languages (often called refinement); variations in ordering arise from different choices of basic event, including for example, refusals and divergences. In both cases, we characterise a theory by its underlying transition system and its choice of ordering. Our treatment is therefore wholly semantic, independent of the syntax and definition of operators of the calculus. We put forward a series of retractions relating the above-mentioned versions of CSP to their corresponding CCS transition models. A retraction is an injection that is (with respect to the chosen ordering) monotonic, increasing and idempotent (up to equivalence). It maps the nodes of a transition system of its source theory to those of a system that has been saturated by additional transitions. Each retraction will be defined by a transition rule, in the style of operational semantics; the proofs use the familiar technique of co-induction, often abbreviated by encoding in the relational calculus. The aim of this paper is to contribute to unification of theories of reactive system programming. More practical benefits may follow. For example, we justify a method to improve the efficiency of model checking based on simulation. Furthermore, we show how model checking of a transition network fits consistently with theorem-proving tools, which reason directly about specifications and designs that are expressed in terms of sets of sequences of observable events.